Math Problem Statement

minus, 4, left parenthesis, minus, 8, w, minus, 4, x, right parenthesis, minus, 7, x, minus, 10, left parenthesis, minus, 10, x, plus, 8, w, right parenthesis−4(−8w−4x)−7x−10(−10x+8w)

Solution

Let's simplify the expression step by step:

Given: 4(8w4x)7x10(10x+8w)-4(-8w - 4x) - 7x - 10(-10x + 8w)

Step 1: Distribute the factors.

First, distribute 4-4 to both terms inside the first parentheses: 4(8w4x)=(32w+16x)-4(-8w - 4x) = (32w + 16x)

Next, distribute 10-10 to both terms inside the second parentheses: 10(10x+8w)=(100x80w)-10(-10x + 8w) = (100x - 80w)

Now substitute these into the original expression: 32w+16x7x+100x80w32w + 16x - 7x + 100x - 80w

Step 2: Combine like terms.

For the ww terms: 32w80w=48w32w - 80w = -48w

For the xx terms: 16x7x+100x=109x16x - 7x + 100x = 109x

Final Expression:

48w+109x-48w + 109x

This is the simplified form of the expression.

Would you like further details on any steps or have any questions?


Relative Questions:

  1. How do we apply the distributive property?
  2. What are like terms, and why can we combine them?
  3. Can the order of terms affect the result in addition and subtraction?
  4. How would this expression change if we added another variable term?
  5. How does factoring differ from distributing?

Tip: Always distribute negative signs carefully to avoid errors in simplification.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Combining Like Terms

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Distributive Law

Suitable Grade Level

Grades 8-10